US6891658B2 - Wide viewing angle reflective display - Google Patents

is a fragmented cross-sectional view, on a greatly enlarged scale, of a portion of an electrophoretically frustrated TIR display in accordance with one embodiment of the invention.

schematically illustrates the wide angle viewing range α of the

apparatus, and the angular range β of the illumination source.

is a cross-sectional view, on a greatly enlarged scale, of a hemispherical portion of one of the spherical high refractive index beads of the

apparatus.

, 3B and 3C depict semi-retro-reflection of light rays perpendicularly incident on the

hemispherical structure at increasing off-axis distances at which the incident rays undergo TIR two, three and four times respectively.

, 4B, 4C, 4D, 4E, 4F and 4G depict the

hemispherical structure, as seen from viewing angles which are offset 0°, 15°, 30°, 45°, 60°, 75°and 90° respectively from the perpendicular.

graphically depicts the angular deviation from true retro-reflection of light rays reflected by the

hemispherical structure. Angular deviation is shown as a function of off-axis distance a normalized such that the radius r=1.

graphically depicts the relative energy distribution, as a function of angular error, of light rays reflected by the

hemispherical structure.

are topographic bottom plan views, on a greatly enlarged scale, of a plurality of hemispherical (

) and approximately hemispherical (

) hemi-beads.

are cross-sectional views, on a greatly enlarged scale, of structures which respectively are not (

) and are (

) approximately hemispherical.

are cross-sectional views, on a greatly enlarged scale, depicting fabrication of high refractive index hemispherical structures on a transparent substrate of arbitrarily low refractive index.

depicts a portion of a front-lit electrophoretically

10 having a transparent

12 formed by partially embedding a large plurality of high refractive index (η₁)

14 in the inward surface of a high refractive index (η₂)

16 having a flat

17 which viewer V observes through an angular range of viewing directions Y. The “inward” and “outward” directions are indicated by double-headed arrow Z.

14 are packed closely together to form an inwardly projecting

18 having a thickness approximately equal to the diameter of one of

14. Ideally, each one of

14 touches all of the beads immediately adjacent to that one bead. As explained below, minimal gaps (ideally, no gaps) remain between adjacent beads.

14 may for example be 40-100 micron diameter high index glass beads available from Potters Industries Inc., Valley Forge, Pa. under the product classification T-4 Sign Beads. Such beads have a refractive index η₁ of approximately 1.90-1.92.

14 may be a nano-polymer composite, for example high refractive index particles suspended in a polymer as described by Kambe et al, in “Refractive Index Engineering of Nano-Polymer Composites”, Materials Research Society Conference, San Francisco, Apr. 16-20, 2001 having a comparably high index η₂ (i.e. η₂ is greater than about 1.75).

An

20 is maintained adjacent the portions of

14 which protrude inwardly from

16 by containment of

20 within a

22 defined by

24. An inert, low refractive index (i.e. less than about 1.35), low viscosity, electrically insulating liquid such as Fluorinert™ perfluorinated hydrocarbon liquid (η₃˜1.27) available from 3M, St. Paul, Minn. is a suitable electrophoresis medium. A bead:liquid TIR interface is thus formed.

20 contains a finely dispersed suspension of light scattering and/or

26 such as pigments, dyed or otherwise scattering/absorptive silica or latex particles, etc.

24's optical characteristics are relatively unimportant:

24 need only form a reservoir for containment of

20 and

26, and serve as a support for

48 as described below.

A small critical angle is preferred at the TIR interface since this affords a large range of angles over which TIR may occur. The relatively large ratio of the index of refraction of beads 14 (η₁˜1.90-1.92) and material 16 (η₂˜1.92) to that of Fluorinert (η₃˜1.27) yields a critical angle of about 41.4°, which is quite small. In the absence of electrophoretic activity, as is illustrated to the right of dashed

28 in

, a substantial fraction (which may be as little as 25%) of the light rays passing through

12 and

14 undergoes TIR at the inward side of

14. For example,

30, 32 are refracted through

16 and

14. As described below, the rays undergo TIR two or more times at the bead:liquid TIR interface, as indicated at

34, 36 in the case of

30; and indicated at

38, 40 in the case of

32. The totally internally reflected rays are then refracted back through

14 and

16 and emerge as

42, 44 respectively, achieving a “white” appearance in each reflection region or pixel.

A voltage can be applied across

20 via

46, 48, which can for example be applied by vapour-deposition to the inwardly protruding surface portion of

14 and to the outward surface of

24.

46 is transparent and substantially thin to minimize its interference with light rays at the bead:liquid TIR interface.

48 need not be transparent. If

20 is activated by actuating

50 to apply a voltage between

46, 48 as illustrated to the left of dashed

28, suspended

26 are electrophoretically moved into the region where the evanescent wave is relatively intense (i.e. within 0.25 micron of the inward surfaces of inwardly protruding

14, or closer). When electrophoretically moved as aforesaid,

26 scatter or absorb light, by modifying the imaginary and possibly the real component of the effective refractive index at the bead:liquid TIR interface. This is illustrated by

52, 54 which are scattered and/or absorbed as they strike

26 inside the evanescent wave region at the bead:liquid TIR interface, as indicated at 56, 58 respectively, thus achieving a “dark” appearance in each non-reflective absorption region or pixel.

As described above, the net optical characteristics of

12 can be controlled by controlling the voltage applied across

20 via

46, 48. The electrodes can be segmented to control the electrophoretic activation of

20 across separate regions or pixels of

12, thus forming an image.

14 and

16 are preferably optically clear—meaning that a substantial fraction of light at normal incidence passes through a selected thickness of the bead or material, with only a small fraction of such light being scattered and/or absorbed by the bead or material. Diminished optical clarity is caused by such scattering and/or absorption, typically a combination of both, as the light passes through the bead or material.

12 need only have a thickness one-half that of beads 14 (i.e. 20 microns for the aforementioned 40 micron beads). A material which is “opaque” in bulk form may nevertheless be “optically clear” for purposes of the invention, if a 10 micron thickness of such material scatters and/or absorbs only a small fraction of normal incident light. Some high refractive index nano-composite polymers have this characteristic and are therefore well suited to use in displays formed in accordance with the invention.

Application of a voltage across

20 by means of

46, 48 and

50 applies electrostatic force on

26, causing them to move into the evanescent wave region as aforesaid. When

26 move into the evanescent wave region they must be capable of frustrating TIR at the bead:liquid interface, by scattering and/or absorbing the evanescent wave. Although

26 may be as large as one micron in diameter, the particles' diameter is preferably significantly sub-optical (i.e. smaller than about 0.25 microns for visible light) such that one or more monolayers of

26 at the TIR interface can entirely fill the evanescent wave region. Useful results are obtained if the diameter of

26 is about one micron, but the display's contrast ratio is reduced because the ability of

26 to pack closely together at the TIR interface is limited by their diameter. More particularly, near the critical angle, the evanescent wave extends quite far into

20, so particles having a diameter of about one micron are able to scatter and/or absorb the wave and thereby frustrate TIR. But, as the angle at which incident light rays strike the TIR interface increases relative to the critical angle, the depth of the evanescent wave region decreases significantly. Relatively large (i.e. one micron) diameter particles cannot be packed as closely into this reduced depth region and accordingly such particles are unable to frustrate TIR to the desired extent. Smaller diameter (i.e. 250 nm) particles can however be closely packed into this reduced depth region and accordingly such particles are able to frustrate TIR for incident light rays which strike the TIR interface at angles exceeding the critical angle.

It is difficult to mechanically frustrate TIR at a non-flat surface like that formed by the inwardly protruding portions of

14, due to the difficulty in attaining the required alignment accuracy between the non-flat surface and the part which is to be mechanically moved into and out of optical contact with the surface. However, electrophoretic medium 20 easily flows to surround the inwardly protruding portions of

14, thus eliminating the alignment difficulty and rendering practical the approximately hemispherically surfaced (“hemi-beaded”) bead:liquid TIR interface described above and shown in FIG. 1A.

In the

embodiment, the refractive index of

14 is preferably identical to that of

16. In such case, only the hemispherical (or approximately hemispherical) portions of

14 which protrude into

20 are optically significant. Consequently,

14 need not be discretely embedded within

16. As explained below, hemispherical (or approximately hemispherical) beads may instead be affixed to a substrate to provide a composite sheet bearing a plurality of inwardly convex protrusions with no gaps, or minimal gaps, between adjacent protrusions and having sufficient approximate sphericity to achieve high apparent brightness through a wide angular viewing range.

It is convenient to explain the invention's wide viewing angle characteristic for the case in which the inwardly convex protrusions are hemispheres.

depicts, in enlarged cross-section, a

60 of one of

14.

60 has a normalized radius r=1 and a refractive index η₁

62 perpendicularly incident (through material 16) on

60 at a radial distance a from

60's centre C encounters the inward surface of

60 at an angle θ₁ relative to

66. For purposes of this theoretically ideal discussion, it is assumed that

16 has the same refractive index as hemisphere 60 (i.e. η₁=η₂), so

62 passes from

16 into

60 without refraction.

62 is refracted at the inward surface of

60 and passes into electrophoretic medium 20 as

64 at an angle θ₂ relative to

66.

Now consider incident

68 which is perpendicularly incident (through material 16) on

60 at a distance

from

60's

68 encounters the inward surface of

60 at the critical angle θ_c (relative to radial axis 70), the minimum required angle for TIR to occur.

68 is accordingly totally internally reflected, as

72, which again encounters the inward surface of

60 at the critical angle θ_c.

72 is accordingly totally internally reflected, as

74, which also encounters the inward surface of

60 at the critical angle θ_c.

74 is accordingly totally internally reflected, as

76, which passes perpendicularly through

60 into the embedded portion of

14 and into

16.

68 is thus reflected back as

76 in a direction approximately opposite that of

68.

All light rays which are perpendicularly incident on

60 at distances a≧a_c from

60's centre C are reflected back, as described above for

68, 76; it being understood that

depicts a theoretically ideal but practically unattainable optically “perfect”

60 which reflects

76 in a direction opposite that of

68. Returning to

, it can be seen that

30, which is reflected back as

42, is another example of such a ray.

, 3B and 3C depict three of optically “perfect”

60's reflection modes. These and other modes coexist, but it is useful to discuss each mode separately.

In

, light rays incident within a range of distances a_c<a≦a₁ undergo TIR twice (the 2-TIR mode) and the reflected rays diverge within a comparatively wide arc φ₁ centred on a direction opposite to the direction of the incident light rays. In

, light rays incident within a range of distances a₁<a≧a₂ undergo TIR three times (the 3-TIR mode) and the reflected rays diverge within a narrower arc φ₂<φ₁ which is again centred on a direction opposite to the direction of the incident light rays. In

, light rays incident within a range of distances a₂<a≧a₃ undergo TIR four times (the 4-TIR mode) and the reflected rays diverge within a still narrower arc φ₃<φ₂ also centred on a direction opposite to the direction of the incident light rays.

60 thus has a “semi-retro-reflective”, partially diffuse reflection characteristic, causing

10 to have a diffuse appearance akin to that of paper.

10 also has a relatively high apparent brightness comparable to that of paper. At normal incidence, the reflectance R of hemisphere 60 (i.e. the fraction of light rays incident on

60 that reflect by TIR) is given by

where η₁ is the refractive index of

60 and η₃ is the refractive index of the medium adjacent the surface of

60 at which TIR occurs. Thus, if

60 is formed of a lower refractive index material such as polycarbonate (η₁˜1.59) and if the adjacent medium is Fluorinert (η₃˜1.27), a reflectance R of about 36% is attained, whereas if

60 is formed of a high refractive index nano-composite material (η₁˜1.92) a reflectance R of about 56% is attained. When illumination source S (

) is positioned behind viewer V's head, the apparent brightness of

10 is further enhanced by the aforementioned semi-retro-reflective characteristic, as explained below.

As shown in

,

60's reflectance is maintained over a broad range of incidence angles, thus enhancing

10's wide angular viewing characteristic and its apparent brightness. For example,

shows

60 as seen from perpendicular incidence—that is, from an incidence angle offset 0° from the perpendicular. In this case, the

80 of

60 for which a≧a_c, appears as an annulus. The annulus is depicted as white, corresponding to the fact that this is the region of

60 which reflects incident light rays by TIR, as aforesaid. The annulus surrounds a

82 which is depicted as dark, corresponding to the fact that this is the non-reflective region of

60 within which incident rays do not undergo TIR.

60 as seen from incidence angles which are respectively offset 15°, 30°, 45°, 60°, 75° and 90° from the perpendicular. Comparison of

with

reveals that the observed area of

80 of

60 for which a≧a_c decreases only gradually as the incidence angle increases. Even at near glancing incidence angles (

) an observer will still see a substantial part of

80, thus giving display 10 a wide angular viewing range over which high apparent brightness is maintained.

further describe the nature of

10's semi-retro-reflective characteristic. “True retro-reflection” occurs when the reflected ray is returned in a direction opposite to that of the incident ray. For purposes of this invention, “semi-retro-reflection” occurs when the reflected ray is returned in a direction approximately opposite to that of the incident ray. Hemispherical reflectors are inherently semi-retro-reflective. In

,

84 represents the angular range of deviation from true retro-reflection of light rays reflected by

60 after undergoing TIR twice (the

2-TIR mode). As expected, the angular deviation is 0° at

That is, in the 2-TIR mode, true retro-reflection occurs if the incident ray encounters

60's TIR interface at an angle of 45°. The angular deviation ranges from about −10° to about 27° as rays vary over the 2-TIR mode incident range for which they are reflected twice. Within this range, apart from the special case of true retro-reflection at 0° angular deviation, the rays are semi-retro-reflected.

FIG. 5A's

86 represents the angular range of deviation from true retro-reflection of light rays reflected by

60 after undergoing TIR three times (the

3-TIR mode). As expected, the angular deviation is 0° at

That is, in the 3-TIR mode, true retro-reflection occurs if the incident ray encounters

60's TIR interface at an angle of 60°. The angular deviation ranges from about −27° to about 18° as rays vary over the 3-TIR mode incident range for which they are reflected three times. Within this range, apart from the special case of true retro-reflection at 0° angular deviation, the rays are semi-retro-reflected.

FIG. 5A's

87 represents the angular range of deviation from true retro-reflection of light rays which are reflected by

60 after undergoing TIR four times (the

4-TIR mode). The angular deviation is 0° at a=0.924=sin 67.5°. That is, in the 4-TIR mode, true retro-reflection occurs if the incident ray encounters

60's TIR interface at an angle of 67.5° . The angular deviation ranges from about −20° to about 15° as rays vary over the 4-TIR mode incident range for which they are reflected four times. Within this range, apart from the special case of true retro-reflection at 0° angular deviation, the rays are semi-retro-reflected.

also depicts curves representing the angular range of deviation from true retro-reflection of light rays which are reflected by

60 after undergoing TIR five, six, seven or more times. Instead of considering these 5-TIR, 6-TIR, 7-TIR and higher modes, it is more useful to consider

, which shows the relative amount (amplitude) of light reflected by

60 as a function of the aforementioned angular deviation. The total area beneath the curve plotted in

corresponds to the cumulative energy of light rays reflected by

60 in all TIR modes.

Every curve plotted in

intersects the 0° angular deviation horizontal axis. Consequently, the cumulative amount of light reflected in all TIR modes reaches a maximum value at 0° angular deviation, as seen in FIG. 5B. The cumulative amount of light reflected in all TIR modes decreases as the magnitude of the aforementioned angular deviation increases, as is also shown in FIG. 5B. Very roughly, approximately one-half of the cumulative reflective energy of light rays reflected by

60 lies within an angular deviation range up to about 10°; and, approximately one-third of the cumulative reflective energy lies within an angular deviation range up to about 5°. Consequently,

10 has very high apparent brightness when the dominant source of illumination is behind the viewer, within a small angular range. This is further illustrated in

which depicts the wide angular range α over which viewer V is able to view

10, and the angle β which is the angular deviation of illumination source S relative to the location of viewer V. Display's 10's high apparent brightness is maintained as long as β is not too large, with the fall-off occurring in proportion to the relative amplitude plotted in FIG. 5B.

Although it may be convenient to fabricate

10 using spherically (or hemispherically) shaped glass beads as aforesaid, a sphere (or hemisphere) may not be the best shape for

14 in all cases. This is because, as shown in

, even if spherical (or hemispherical)

14 are packed together as closely as possible within monolayer 18 (FIG. 1A),

78 unavoidably remain between adjacent beads. Light rays incident upon any of

78 are “lost”, in the sense that they pass directly into

20, producing undesirable dark spots on viewing

17. While these spots are invisibly small, and therefore do not detract from

10's appearance, they do detract from viewing

17's net average reflectance.

depicts alternative “approximately hemispherical”, inwardly convex “hemi-beads” 14A which are substantially hexagonal in an outward-most cross-sectional region parallel to the macroscopic plane of

10's viewing surface 17 (FIG. 1A), allowing hemi-

14A to be packed closely together with no gaps, or minimal gaps, between adjacent ones of hemi-

14A. The inwardmost regions of hemi-

14A, (“inward” again being the side of hemi-

14A which protrudes into medium 20) are semi-spherical, as indicated by the innermost circular topographic lines on hemi-

14A. Between their semi-spherical inward-most regions and their hexagonal outwardmost regions, the shape of each bead hemi-14A varies from semi-spherical to hexagonal, as indicated by the intermediate topographic lines on hemi-

14A. The closer a particular region of hemi-

14A is to the inwardmost semi-spherical region, the more spherical that particular region's shape is. Conversely, the closer a particular region of hemi-

14A is to the outwardmost hexagonal region, the more hexagonal that particular region's shape is.

Although hemi-

14A may have a slightly reduced reflectance and may exhibit slightly poorer semi-retro-reflection characteristics, this may be more than offset by the absence of gaps. Hemi-

14A may have many other alternative irregular shapes yet still achieve acceptably high apparent brightness throughout acceptably wide angular viewing ranges. Useful shapes include those which are approximately hemispherical (“hemi-beads”), in the sense that such a shape's surface normal at any point differs in direction from that of a similarly sized “perfect” hemisphere by an error angle ε which is small. This is illustrated in

.

The solid line portion of

depicts a

88 which is not “approximately hemispherical”, even though it closely matches the dimensions of a substantially identically-sized notionally “perfect”

90 shown in dashed outline and superimposed on

88.

88 has a surface normal 92 at a selected point 94 on

88.

90 has a surface normal 96 (i.e. radius) at

98, which is the closest point on

90 to selected point 94 (in this example, points 94, 98 happen to coincide at a point where

88 intersects hemisphere 90).

92, 96 differ in direction by a relatively substantial error angle ε₁. By contrast, the solid line portion of

depicts a hemi-

98 which is “approximately hemispherical”. Hemi-

98 has a surface normal 100 at a selected

102 on hemi-

98. The dashed line portion of

depicts a notional “perfect” hemisphere 104 having a size substantially identical to and superimposed on hemi-

98. Hemisphere 104 has a surface normal 106 (i.e. radius) at

108, which is the closest point on hemisphere 104 to selected

102.

100, 106 differ in direction by a relatively insubstantial error angle ε₂ which is preferably less than 10° and ideally substantially less than 10°.

As previously mentioned, instead of partially embedding spherical (or approximately spherical) beads in a material, one may instead form hemispherical (or approximately hemispherical) beads on a substrate to provide a composite sheet bearing a plurality of inwardly convex protrusions with no gaps, or minimal gaps, between adjacent protrusions and having sufficient approximate sphericity to achieve high apparent brightness through a wide angular viewing range. Specifically, high refractive index hemispherical (or approximately hemispherical) beads may be affixed to a low refractive index transparent substrate (i.e. η₁>>η₂, for example η₁≈1.92 and η_2≈1.59) to provide a high apparent brightness, wide angular viewing range display in accordance with the invention. Fabrication of such a display is illustrated in

.

As shown in

, a large number of the aforementioned high refractive index T-4

110 of varying sizes (as supplied by the manufacturer) are pressed into the surface of an adhesive

112, producing a

114. A predetermined uniform pressure suffices to embed one-half of a sphere in an elastomer, independently of the sphere's size. Accordingly, application of a predetermined uniform pressure embeds one-half of most of

110 in

112, as shown in FIG. 8A. Provision of

110 in varying sizes is advantageous, in that a greater net coverage area can be attained than with spheres of identical size.

Next, as shown in

, beaded

114 is pressed onto and reciprocated against flat optical polishing surface 116 (for example 1 micron diamond grit embedded in brass) as indicated by double-headed arrow 118 (FIGS. 8B and 8C), until

110 are abraded to the point that only hemispheres 120 remain embedded in

112, with polished, substantially flat, substantially coplanar circular faces 122 exposed (FIG. 8D).

122 are then adhered (for example, using a spin-coated ultra-violet cured epoxy) to a transparent

124 such as polycarbonate (η˜1.59) (FIG. 8E), and

112 is removed, for example by means of a suitable solvent, yielding the desired hemi-beaded structure 126 (

) consisting of high refractive index hemispherical (or approximately hemispherical)

120 on

124.

126 can then be indium-tin-oxide (ITO) coated to produce a transparent electrode on

120, as previously mentioned. Alternatively,

110 can be ITO-coated before they are pressed into

112, then hemispheres 120 can be electrically connected to one another by depositing, around their bases a thin conductive coating such as Bayer Baytron™ conductive polymer.

High apparent brightness, wide angular viewing range displays can also be produced in accordance with the invention by selectably frustrating TIR in alternative ways. For example, instead of suspending

26 in

20, one could suspend an electrode-bearing membrane in the medium as disclosed in WO01/37627 which is incorporated herein by reference. TIR can also be selectably frustrated without using electrophoresis and without providing any liquid adjacent the “hemi-beaded” TIR interface. For example, as disclosed in U.S. Pat. Nos. 5,959,777; 5,999,307; and 6,088,013 (all of which are incorporated herein by reference) a member can be controllably deformed or positioned by hydraulic, pneumatic, electronic, electrostatic, magnetic, magneto-strictive, piezoelectric, etc. means such that the member either is or is not in optical contact with a selected “pixel” portion of the hemi-beaded TIR interface.

1. A reflective display, comprising:

(a) a plurality of approximately hemispherical transparent hemi-beads selectively different from a national perfect hemisphere, the hemi-beads having a refractive index η₁ substantially covering and protruding inwardly from an inward surface of a transparent sheet having a refractive index η₂, said transparent sheet having an outward viewing surface; and,

(b) means for selectably moving a member into an intense evanescent wave region at an inward side of said hemi-beads to selectably frustrate substantial total internal reflection of light rays at said inward side of said hemi-beads.

2. A display as defined in

, wherein a first surface normal at substantially any selected point on substantially any selected one of said hemi-beads differs in direction by an angle ε from a second surface normal at a notional point on a notional perfect hemisphere superimposed on said selected one of said hemi-beads, said notional perfect hemisphere and said selected one of said hemi-beads having a substantially equal size, said notional point being the point on said notional perfect hemisphere which is closest to said selected point, and wherein ε is less than a predefined value.

3. A display as defined in

, wherein said hemi-beads are approximately hemispherical portions of approximately spherical members partially embedded in said transparent sheet.

4. A display as defined in

, wherein said hemi-beads are approximately hemispherical portions of approximately spherical members partially embedded in said transparent sheet.

5. A display as defined in

, wherein said hemi-beads are approximately hemispherical members affixed to said inward surface of said transparent sheet.

6. A display as defined in

, wherein said hemi-beads are approximately hemispherical members affixed to said inward surface of said transparent sheet.

7. A display as defined in

, wherein η₁≈η₂.

8. A display as defined in

, wherein η₁≈η₂.

9. A display as defined in any one of claims 1-8, wherein said transparent sheet further comprises a nano-composite structure of high refractive index particles suspended in a polymer.

10. A display as defined in any one of claims 1-8, wherein said hemi-beads are shaped to minimize gaps between outwardmost portions of adjacent ones of said hemi-beads.

11. A display as defined in any one of claims 1-8, wherein:

(i) said transparent sheet further comprises a nano-composite structure of high refractive index particles suspended in a polymer; and,

(ii) said hemi-beads are shaped to minimize gaps between outwardmost portions of adjacent ones of said hemi-beads.

12. A display as defined in

, further comprising:

(a) a second sheet spaced inwardly from said transparent sheet to define a reservoir between said transparent sheet and said second sheet;

(b) an electrophoresis medium within said reservoir, said medium having a refractive index η₃;

(c) a first electrode on said inward side of said hemi-beads;

(d) a second electrode on an outward side of said second sheet;

13. A display as defined in

, said member further comprising a plurality of light absorptive particles suspended in said medium.

14. A display as defined in

, wherein said medium is a perfluorinated hydrocarbon liquid.

15. A display as defined in

, wherein a first surface normal at substantially any selected point on substantially any selected one of said hemi-beads differs in direction by an angle ε from a second surface normal at a notional point on a notional perfect hemisphere superimposed on said selected one of said hemi-beads, said notional perfect hemisphere and said selected one of said hemi-beads having a substantially equal size, said notional point being the point on said notional perfect hemisphere which is closest to said selected point, and wherein ε is less than a predefined value.

16. A display as defined in

, wherein said hemi-beads are approximately hemispherical portions of approximately spherical members partially embedded in said transparent sheet.

17. A display as defined in

, wherein said hemi-beads are approximately hemispherical members affixed to said inward surface of said transparent sheet.

18. A display as defined in

, wherein η₁≈η₂.

19. A display as defined in

, wherein η₁≈η₂≈1.92 and η₃≈1.27.

20. A display as defined in any one of claims 12-17, wherein said transparent sheet further comprises a nano-composite structure of high refractive index particles suspended in a polymer.

21. A display as defined in any one of claims 12-17, wherein said hemi-beads are shaped to minimize gaps between outwardmost portions of adjacent ones of said hemi-beads.

22. A display as defined in any one of claims 12-17, wherein:

(i) said transparent sheet further comprises a nano-composite structure of high refractive index particles suspended in a polymer; and,

(ii) said hemi-beads are shaped to minimize gaps between outwardmost portions of adjacent ones of said hemi-beads.

23. A display as defined in

, said member further comprising an elastomer controllably positionable between a first position in which said elastomer is within said intense evanescent wave region and a second position in which said elastomer is not within said intense evanescent wave region.

24. A display as defined in

, said member further comprising an elastomer controllably deformable between a first position in which said elastomer is within said intense evanescent wave region and a second position in which said elastomer is not within said intense evanescent wave region.

25. A method of making a reflective display, said method comprising:

(a) partially embedding a plurality of approximately spherical high refractive index beads in one side of an elastomeric substrate;

(b) removing portions of said beads which are not embedded in said substrate to produce a plurality of approximately hemispherical high refractive index hemi-beads embedded in said substrate, said hemi-beads having substantially flat, substantially coplanar faces;

(c) transparently adhering said hemi-bead coplanar faces to a transparent substrate; and,

(d) removing said elastomeric substrate.

26. A method as defined in

, wherein said partially embedding further comprises distributing said plurality of approximately spherical beads over said side of said elastomeric substrate and applying a predetermined uniform pressure to said approximately spherical beads to embed approximately one-half of substantially each one of said approximately spherical beads in said side of said elastomeric substrate.

27. A method as defined in

, wherein said removing portions of said beads further comprises abrading said portions of said beads which are not embedded in said substrate by reciprocation against a flat optical polishing surface.

28. A method as defined in

, wherein said adhering further comprises transparent adhesive bonding.

29. A method as defined in

, wherein said adhering further comprises transparent adhesive bonding with a transparent spin-coated ultra-violet cured epoxy.

30. A method as defined in

, wherein said removing said elastomeric substrate further comprises peeling said elastomeric substrate away from said hemi-beads.

31. A method as defined in

, wherein said removing said elastomeric substrate further comprises dissolving said elastomeric substrate in a solvent.

32. An image display method, comprising:

(a) forming an approximately hemispherical transparent hemi-bead, selectively different from a national perfect hemisphere, the hemi-beads having a refractive index η₁; and,

(b) selectably moving a member into an intense evanescent wave region at an inwardly convex side of said hemi-bead to selectably frustrate substantial total internal reflection of light rays at said inwardly convex side of said hemi-bead.

said notional perfect hemisphere and said hemi-bead having a substantially equal size, said notional point being the point on said notional perfect hemisphere which is closest to said selected point.

34. An image display method as defined in

, wherein said forming further comprises embedding an approximately hemispherical portion of an approximately spherical member in a transparent sheet.

35. An image display method as defined in

, further comprising applying an outward side of said hemi-bead to an inward surface of a transparent sheet having a refractive index η₂.

36. An image display method as defined in

, wherein η₁≈η₂.

37. An image display method as defined in

, further comprising forming said transparent sheet as a nano-composite structure of high refractive index particles suspended in a polymer.

38. An image display method as defined in

, further comprising forming a substantially coplanar plurality of said hemi-beads and minimizing gaps between outwardmost portions of adjacent ones of said hemi-beads.

39. An image display method as defined in

, further comprising:

(a) spacing a sheet inwardly from said hemi-beads to define a reservoir between said hemi-beads and said sheet;

(b) providing an electrophoresis medium within said reservoir, said medium having a refractive index η₃;

(c) providing said member within said medium;

40. An image display method as defined in

, further comprising:

(a) forming a first electrode on said inwardly convex side of said hemi-beads;

(b) forming a second electrode on an outward side of said sheet; and,

(c) applying said voltage between said electrodes.

41. An image display method as defined in

, further comprising providing said member as a plurality of light absorptive particles suspended in said medium.

42. An image display method as defined in

, further comprising providing said medium as a perfluorinated hydrocarbon liquid.

43. An image display method as defined in

, wherein η₁≈1.92 and η₂≈1.27.